What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle BDE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{BD} \cong \overline{CF}$ $, \ $ $ \angle DBE \cong \angle CFE$ $, \ $ $ \overline{BE} \cong \overline{EF}$ $, \ $ $ \angle DBE \cong \angle ABC$ $, \ $ $ \overline{BE} \cong \overline{AB}$ $, \ $ and $\ $ $ \angle BED \cong \angle BAC$ Proof $ \triangle FCE \cong \triangle BDE$ because SAS $ \angle BDE \cong \angle BEC$ because vertical angles are equal $ \angle BCE \cong \angle CEF$ because alternate interior angles are equal $ \angle BDE \cong \angle BEC$ because vertical angles are equal $ \triangle BDE \cong \triangle BCA$ because ASA $ \triangle BCE \cong \triangle BDE$ because SSS
Explanation: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle BEC \cong \angle BDE$ is the first wrong statement.